Related papers: An action for nonlinear dislocation dynamics
A dual variational principle is defined for the nonlinear system of PDE describing the dynamics of dislocations in elastic solids. The dual variational principle accounting for a specified set of initial and boundary conditions for a…
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase…
A full selfconsistent set of equations is deduced to describe the kinetics and dynamics of charged quasiparticles (electrons, holes etc.) with arbitrary dispersion law in crystalline solids subjected to time-varying deformations. The set…
A novel, concurrent multiscale approach to meso/macroscale plasticity is demonstrated. It utilizes a carefully designed coupling of a partial differential equation (pde) based theory of dislocation mediated crystal plasticity with…
We present a microscopic derivation of the nonlinear fluctuating hydrodynamic equation for the homogeneous crystalline solid from the Hamiltonian description of a many-particle system. We propose a microscopic expression of the displacement…
A part of the theory of dislocations in crystals is revised with the aim to fit it into the framework of the nonlinear theory of plasticity initially designed for amorphous glassy materials.
By means of linear theory of elastoplasticity, solutions are given for screw and edge dislocations situated in an isotropic solid. The force stresses, strain fields, displacements, distortions, dislocation densities and moment stresses are…
Dislocations, line defects in crystalline materials, play an essential role in the mechanical[1,2], electrical[3], optical[4], thermal[5], and phase transition[6] properties of these materials. Dislocation motion, an important mechanism…
The dynamics and thermodynamics of dislocated crystals are studied within the framework of the nonlinear theory of elastic and plastic deformations.
This paper examines a system of partial differential equations describing dislocation dynamics in a crystalline solid. In particular we consider dynamics linearized about a state of zero stress and use linear semigroup theory to establish…
A consistent, small scale description of plastic motion in a crystalline solid is presented based on a phase field description. By allowing for independent mass motion given by the phase field, and lattice distortion, the solid can remain…
Drag and diffusion of mobile ions in solids are of interest for both purely theoretical and applied scientific communities. This article proposes a theoretical description of ion drag in solids that can be used to estimate ionic…
We develop and demonstrate the first general computational tool for finite deformation static and dynamic dislocation mechanics. A finite element formulation of finite deformation (Mesoscale) Field Dislocation Mechanics theory is presented.…
A phase field model of a crystalline material at the mesoscale is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. We first obtain the elastic stress from the phase field free energy…
Plastic deformation In crystalline materials is controlled by the motion and interactions of dislocations [AND 17]. Discrete Dislocation Dynamics (DDD) simulations have now existed for about 25 years to investigate plastic flow at the…
The mechanical behaviors of polycrystalline solids are determined by the interplay between phenomena governed by two different thermodynamic temperatures: the configurational effective temperature that controls the density of dislocations,…
This review is a simplified summary of the thermodynamic dislocation theory, with special emphasis on the role of an effective temperature. Materials scientists, for decades, have asserted that statistical thermodynamics is not applicable…
Understanding plastic deformation of crystals in terms of the fundamental physics of dislocations has remained a grand challenge in materials science for decades. To overcome this, the Discrete Dislocation Dynamics (DDD) method has been…
We develop a fully coupled theoretical description of dislocation dynamics on deformable crystalline surfaces, using continuum modeling and the amplitude-phase-field crystal (APFC) framework extended to curved geometries. We derive a…